Problem: Simplify the following expression: $ x = \dfrac{8}{r + 7} - 5 $
In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{r + 7}{r + 7}$ $ \dfrac{-5}{1} \times \dfrac{r + 7}{r + 7} = \dfrac{-5r - 35}{r + 7} $ Therefore $ x = \dfrac{8}{r + 7} + \dfrac{-5r - 35}{r + 7} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{8 - 5r - 35}{r + 7} $ $x = \dfrac{-5r - 27}{r + 7}$